Stems from Schweser Volume 2 Exam 1 Afternoon Session question 49. Given Portfolio is beta adjusted by use of futures. After 6 months portfolio values are reevaluted and it is asked for effective beta.
Regular formula is
Effective Beta = % change in value of portfolio / % change in value of index
But in this case with 6 months past I was wondering if you should theoretically incorporate the risk free rate and reduce the observed returns by it, since beta should only effect the excess return:
E® = RFR + Beta * ( Return of Market - RFR)
Other examples were more about instantenious changes. Since a risk free rate was not given, it does not seem to be relevant, but I was quite confused doing the exam. Anybody has any thoughts on this?
You’re mixing up beta as a measure of systematic risk (regressing returns of an asset versus a benchmark) and beta as defined by CAPM (risk premium). The question is dealing with the former.
Effective beta is useful to use to determine how effective your hedge was (i.e. %∆Value of the hedged portfolio/%∆ in market). When your effective beta is different than your target beta it can be because of rounding contracts, examining the % change prior to expiration, a hedging instrument that doesn’t perfectly fit the portfolio etc.
As arbman said your other beta is measuring the sensitivity of a security to changes in the market.
Do these two approaches result in different beta figures for the same security / portfolio? My understanding is these are two definitions yielding the same number and are used interchangeably as appropriate?
Just checking on the internet I guess the regression of return of stock against return on benchmark to come to beta seems to be a simplification. Probably does not change the results very much but from a theoretical point of view I would argue to incorporate the risk free rate
“YCharts calculates the 60 month market beta by regressing stock returns less the risk free rate of returns on the market returns less the risk free rate of return”
Hi , yes this is a confusion . Ideally it should be excess return regression , but I understand as we assume risk free rate to be constant in CAPM it doesn’t matter in calculating slope. That’s my thought .